Complicated Truth Tables

Truth tables are an algorithmic method of discovering when complex statements are true based on their simple sentences. When the number of simple sentences is small, running the algorithm is easy enough. However, the level of complexity grows exponentially. Indeed, the number of rows in a truth table is 2^n, where n is the number of premises. Thus, even if you only have four premises, you already need to have sixteen rows. This motivates an alternative method of proofs that we build toward in the next lectures.